论文标题
涉及非convex $ \ ell_ {q，p} $正则化的结构化优化的筛选策略
A Screening Strategy for Structured Optimization Involving Nonconvex $\ell_{q,p}$ Regularization
论文作者
论文摘要
在本文中，我们制定了一种简单而有效的筛选策略，以提高涉及非convex $ \ ell_ {q，p} $正则化的结构化优化方面的计算效率。基于迭代重新加权的$ \ ell_1 $（irl1）框架，所提出的筛选规则就像一个预处理模块一样工作，该模块可能会在启动子问题求解器之前可能会删除非活动组，从而减少总计计算时间。这主要是通过在每次迭代期间启发双重子问题信息来实现的。此外，我们证明我们的筛选规则可以在IRL1方法的有限数量的迭代中删除所有不活动变量。数值实验说明了与几种最新算法相比，我们的筛选规则策略的效率。
In this paper, we develop a simple yet effective screening rule strategy to improve the computational efficiency in solving structured optimization involving nonconvex $\ell_{q,p}$ regularization. Based on an iteratively reweighted $\ell_1$ (IRL1) framework, the proposed screening rule works like a preprocessing module that potentially removes the inactive groups before starting the subproblem solver, thereby reducing the computational time in total. This is mainly achieved by heuristically exploiting the dual subproblem information during each iteration.Moreover, we prove that our screening rule can remove all inactive variables in a finite number of iterations of the IRL1 method. Numerical experiments illustrate the efficiency of our screening rule strategy compared with several state-of-the-art algorithms.
